Emissivity Table: Emissivity of Metals, Anodized Aluminium and Coatings

What is emissivity? Definition

• Symbol: ε (epsilon), dimensionless. For real surfaces the term emittance is also used, in German Emissionsgrad.
• The reference is the black body. At every temperature and wavelength it emits the maximum thermal radiation physically possible (Stefan-Boltzmann law).
• Table values are usually total emissivities, either averaged over all directions (hemispherical) or measured perpendicular to the surface (normal). The difference is typically a few hundredths.
• For heat sinks at 20 to 100 °C, treating the surface as a gray body, i.e. with ε independent of wavelength, is a common and adequate approximation.

Emissivity table: values for metals, anodized aluminium and coatings

The table shows typical emissivities at about 20 to 100 °C in the long-wave infrared, which is where heat sinks and electronics radiate their heat. Values vary with source, measurement method and sample. For accurate measurements or designs, determine the emissivity on the actual part.

Sources: VDI Heat Atlas (chapter on thermal radiation); Incropera et al., Fundamentals of Heat and Mass Transfer (appendix tables); Modest, Radiative Heat Transfer; Henninger, NASA Reference Publication 1121 (1984) for anodic coatings; emissivity tables from thermal imaging camera manufacturers. The ranges summarize these sources and should be read as guide values.

Emissivity of aluminium and anodized aluminium

Aluminium is the standard material for heat sinks. Depending on the surface, its emissivity ranges from below 0.05 to above 0.9.

• Bare, polished or mill-finish aluminium is at about 0.03 to 0.10. Untreated extrusions radiate very little heat and cannot be measured directly with a thermal camera.
• The natural oxide skin that forms in air changes little. Only heavily oxidized surfaces reach about 0.2 to 0.3.
• Anodizing changes the picture: the anodic aluminium oxide layer emits very well in the long-wave infrared. Clear anodized aluminium is at about 0.6 to 0.9, black anodized at 0.85 to 0.95.
• Whether black, colored or clear is secondary in the infrared. Layer thickness is what counts. Dyed layers need a certain minimum thickness for even coloring, which is why tables often list them slightly higher.
• Powder coating and paint reach similarly high values of about 0.85 to 0.95, but build up thicker than an anodic layer.

Emissivity of copper, brass and stainless steel

• Polished copper is at about 0.02 to 0.05, at the very bottom of all engineering surfaces. In air, copper tarnishes over time and ε rises as the oxide layer grows. Heavily oxidized copper reaches 0.6 to 0.8, black oxidized copper up to about 0.88.
• For thermal images of copper cold plates, busbars or copper inlays, always check the surface condition. The same material can range from 0.03 to 0.8 depending on the age of the surface.
• Brass behaves similarly: about 0.03 to 0.05 when polished, 0.2 to 0.6 when tarnished or oxidized.
• Polished stainless steel, at about 0.07 to 0.2, is somewhat higher than aluminium and copper but remains a poor emitter. Stainless steel oxidized at high temperature reaches 0.5 to 0.85.
• Nickel-plated and tin-plated surfaces remain metallic at about 0.04 to 0.15. They protect against corrosion and improve solderability, but they do not improve radiation.

What does emissivity depend on?

Unlike thermal conductivity, emissivity is not a pure material constant. It describes a surface and changes with its condition, with temperature and with wavelength.

Kirchhoff's law: emissivity equals absorptivity

According to Kirchhoff's law of thermal radiation, the absorptivity α of a surface equals its emissivity ε at the same wavelength λ, direction and temperature T. A surface that absorbs a given wavelength well therefore also emits it well:

• For opaque bodies with reflectivity ρ, α + ρ = 1 also applies, and therefore ε = 1 − ρ. What reflects infrared well radiates poorly. That is why polished metals have such low emissivities.
• The equality only holds at the same wavelength. Sunlight lies mostly between 0.3 and 2.5 µm, the radiation emitted by a heat sink around 10 µm.
• White paint therefore absorbs only about 20 to 30 % of sunlight but emits in the infrared with ε ≈ 0.9. Black anodized surfaces absorb considerably more heat in the sun than light ones.

Why emissivity matters for heat sinks

A heat sink releases heat to its surroundings by convection and radiation. How large the radiation share is depends mainly on whether the air flows freely or is forced.

• Natural convection: without a fan, the heat transfer coefficient is usually only about 3 to 10 W/(m²·K). A black anodized heat sink then transfers a noticeable share of its heat by radiation. Figures of around 20 to 30 % are often quoted, depending on temperature, fin geometry and surroundings.
• Bare aluminium with ε ≈ 0.05, by contrast, hardly radiates at all. For passive heat sinks, anodizing or painting therefore brings a real thermal benefit.
• Forced convection: with a fan, the heat transfer coefficient rises to typically 25 to 100 W/(m²·K) or more. The radiation share drops to a few percent, and the finish is then mainly a question of corrosion protection and appearance.
• Fin arrays: facing fins are at almost the same temperature and radiate at each other. Net heat is only released by the part that sees the surroundings. Relative to the total fin area, the effective emissivity of a fin array is therefore much lower than the surface value. For a rough estimate, calculate the radiation using the envelope area of the heat sink.
• More fins enlarge the convective area but hardly the radiation. Very narrow fin spacing also slows the airflow, which is why passive heat sinks have an optimum fin spacing.
• Surroundings: in a closed enclosure, the temperature of the enclosure wall is what counts. The warmer the wall, the less heat leaves by radiation. In direct sunlight, dark surfaces also absorb additional heat.
• The anodic layer itself is only a few micrometers thick. Its additional thermal resistance is negligible compared with the transfer to the air.

Calculating thermal radiation: formula and worked example

The net heat flow that a surface radiates to much larger surroundings follows from the Stefan-Boltzmann law:

• Q̇: net radiated heat flow [W]
• ε: emissivity of the surface [–]
• σ: Stefan-Boltzmann constant, 5.670 · 10⁻⁸ W/(m²·K⁴)
• A: radiating area [m²]
• T₁, T₂: absolute temperature of surface and surroundings [K], i.e. °C + 273.15

The formula applies to a gray surface that fully sees large surroundings (view factor 1), such as a free-standing plate in a room. Always use temperatures in kelvin, with °C the result is wrong.

Worked example: bare vs. black anodized aluminium

A cooling surface of 100 cm² is at 60 °C, the surroundings at 25 °C. How much heat does it radiate, once bare (ε = 0.05) and once black anodized (ε = 0.85)?

1. T₁ = 60 °C = 333.15 K; T₂ = 25 °C = 298.15 K; A = 100 cm² = 0.01 m²
2. T₁⁴ − T₂⁴ = 1.232 · 10¹⁰ K⁴ − 0.790 · 10¹⁰ K⁴ = 4.42 · 10⁹ K⁴
3. Black body (ε = 1): σ · A · (T₁⁴ − T₂⁴) = 5.670 · 10⁻⁸ · 0.01 · 4.42 · 10⁹ ≈ 2.50 W
4. Bare aluminium (ε = 0.05): Q̇ ≈ 0.05 · 2.50 W ≈ 0.13 W
5. Black anodized (ε = 0.85): Q̇ ≈ 0.85 · 2.50 W ≈ 2.13 W

The anodized surface radiates about 17 times as much heat as the bare one. For comparison: natural convection removes about 1.8 to 2.8 W from the same surface at a heat transfer coefficient of 5 to 8 W/(m²·K). On a flat, freely radiating surface, radiation is therefore of the same order of magnitude as convection.

Setting emissivity correctly on a thermal imaging camera

A thermal camera measures radiation, not temperature. It converts back to surface temperature using the emissivity you set. If ε is wrong, the displayed temperature is wrong too.

• Besides ε, the reflected apparent temperature belongs in the camera settings, usually the ambient temperature. At longer distances, distance and humidity come into play as well.
• Bare metals with ε below about 0.2 cannot be measured reliably in practice. They mainly mirror their surroundings, and even small errors in ε lead to large temperature errors.
• Remedy: apply tape or matte paint of known emissivity (often about 0.95, check the manufacturer's data) to the measuring point, wait for thermal equilibrium and measure there.
• Alternatively, measure at the same spot with a thermocouple and adjust ε on the camera until both readings match.
• Measure as perpendicular to the surface as possible. At grazing angles, emissivity changes, noticeably beyond about 60° from the surface normal.
• Use values for the camera's wavelength band. Manufacturer tables list black anodized aluminium at 70 °C at about 0.95 in the long-wave band (about 8 to 14 µm), but only about 0.67 in the short-wave band.
• Glass is opaque in the long-wave infrared. Through a window, the camera measures the pane, not the object behind it.

Related calculators and topics

• Calculate heat flow, including radiation →
• Heat transfer coefficient: values and formulas →
• Thermal conductivity: table for metals →
• Calculate thermal resistance (Rth) →
• Limits of air cooling →
• Electronics cooling overview →
• Surface finishing: anodizing and coatings →
• Heat sinks for power electronics →